| Title:
|
Lower bounds on signed edge total domination numbers in graphs (English) |
| Author:
|
Karami, H. |
| Author:
|
Sheikholeslami, S. M. |
| Author:
|
Khodkar, Abdollah |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
595-603 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The open neighborhood $N_G(e)$ of an edge $e$ in a graph $G$ is the set consisting of all edges having a common end-vertex with $e$. Let $f$ be a function on $E(G)$, the edge set of $G$, into the set $\{-1, 1\}$. If $ \sum _{x\in N_G(e)}f(x) \geq 1$ for each $e\in E(G)$, then $f$ is called a signed edge total dominating function of $G$. The minimum of the values $\sum _{e\in E(G)} f(e)$, taken over all signed edge total dominating function $f$ of $G$, is called the signed edge total domination number of $G$ and is denoted by $\gamma _{st}'(G)$. Obviously, $\gamma _{st}'(G)$ is defined only for graphs $G$ which have no connected components isomorphic to $K_2$. In this paper we present some lower bounds for $\gamma _{st}'(G)$. In particular, we prove that $\gamma _{st}'(T)\geq 2-m/3$ for every tree $T$ of size $m\geq 2$. We also classify all trees $T$ with $\gamma _{st}'(T)=2-m/3$. (English) |
| Keyword:
|
signed edge domination |
| Keyword:
|
signed edge total dominating function |
| Keyword:
|
signed edge total domination number |
| MSC:
|
05C05 |
| MSC:
|
05C69 |
| idZBL:
|
Zbl 1174.05095 |
| idMR:
|
MR2455925 |
| . |
| Date available:
|
2010-07-20T13:54:10Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140408 |
| . |
| Reference:
|
[1] Karami, H., Khodkar, A., Sheikholeslami, S. M.: Signed edge domination numbers in trees.Ars Combinatoria (to appear). MR 2568858 |
| Reference:
|
[2] West, D. B.: Introduction to Graph Theory.Prentice-Hall, Inc (2000). MR 1367739 |
| Reference:
|
[3] Xu, B.: On signed edge domination numbers of graphs.Discrete Mathematics 239 (2001), 179-189. Zbl 0979.05081, MR 1850997, 10.1016/S0012-365X(01)00044-9 |
| Reference:
|
[4] Xu, B.: On lower bounds of signed edge domination numbers in graphs.J. East China Jiaotong Univ. 1 (2004), 110-114 Chinese. |
| Reference:
|
[5] Zelinka, B.: On signed edge domination numbers of trees.Math. Bohem. 127 (2002), 49-55. Zbl 0995.05112, MR 1895246 |
| . |
